Analytical transformations in minimizing logical functions

Author(s):  
Anvar Kabulov ◽  
Aziz Ashurov ◽  
Mansur Berdimurodov
Keyword(s):  
Author(s):  
Fred V. Brock ◽  
Scott J. Richardson

This book treats instrumentation used in meteorological surface systems, both on the synoptic scale and the mesoscale, and the instrumentation used in upper air soundings. The text includes material on first- and second-order differential equations as applied to instrument dynamic performance, and required solutions are developed. Sensor physics are emphasized in order to explain how sensors work and to explore the strengths and weaknesses of each design type. The book is organized according to sensor type and function (temperature, humidity, and wind sensors, for example), though several unifying themes are developed for each sensor. Functional diagrams are used to portray sensors as a set of logical functions, and static sensitivity is derived from a sensor's transfer equation, focusing attention on sensor physics and on ways in which particular designs might be improved. Sensor performance specifications are explored, helping to compare various instruments and to tell users what to expect as a reasonable level of performance. Finally, the text examines the critical area of environmental exposure of instruments. In a well-designed, properly installed, and well-maintained meteorological measurement system, exposure problems are usually the largest source of error, making this chapter one of the most useful sections of the book.


Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Vedhas Pandit ◽  
Björn Schuller

We present a new technique for defining, analysing, and simplifying digital functions, through hand-calculations, easily demonstrable therefore in the classrooms. It can be extended to represent discrete systems beyond the Boolean logic. The method is graphical in nature and provides complete ‘‘implementation-free” description of the logical functions, similar to binary decision diagrams (BDDs) and Karnaugh-maps (K-maps). Transforming a function into the proposed representations (also the inverse) is a very intuitive process, easy enough that a person can hand-calculate these transformations. The algorithmic nature allows for its computing-based implementations. Because the proposed technique effectively transforms a function into a scatter plot, it is possible to represent multiple functions simultaneously. Usability of the method, therefore, is constrained neither by the number of inputs of the function nor by its outputs in theory. This, being a new paradigm, offers a lot of scope for further research. Here, we put forward a few of the strategies invented so far for using the proposed representation for simplifying the logic functions. Finally, we present extensions of the method: one that extends its applicability to multivalued discrete systems beyond Boolean functions and the other that represents the variants in terms of the coordinate system in use.


2018 ◽  
Vol 8 (6) ◽  
pp. 20180029 ◽  
Author(s):  
Andrew Adamatzky

We propose that fungi Basidiomycetes can be used as computing devices: information is represented by spikes of electrical activity, a computation is implemented in a mycelium network and an interface is realized via fruit bodies. In a series of scoping experiments, we demonstrate that electrical activity recorded on fruits might act as a reliable indicator of the fungi’s response to thermal and chemical stimulation. A stimulation of a fruit is reflected in changes of electrical activity of other fruits of a cluster, i.e. there is distant information transfer between fungal fruit bodies. In an automaton model of a fungal computer, we show how to implement computation with fungi and demonstrate that a structure of logical functions computed is determined by mycelium geometry.


2017 ◽  
pp. 385-399
Author(s):  
Mark Conway Munro
Keyword(s):  

Author(s):  
Wlodzislaw Duch ◽  
◽  
Rafal Adamczak ◽  
KrzysAof Grabczewski ◽  
Grzegorz Zal

Methodology of extraction of optimal sets of logical rules using neural networks and global minimization procedures has been developed. Initial rules are extracted using density estimation neural networks with rectangular functions or multilayered perceptron (MLP) networks trained with constrained backpropagation algorithm, transforming MLPs into simpler networks performing logical functions. A constructive algorithm called CMLP2LN is proposed, in which rules of increasing specificity are generated consecutively by adding more nodes to the network. Neural rule extraction is followed by optimization of rules using global minimization techniques. Estimation of confidence of various sets of rules is discussed. The hybrid approach to rule extraction has been applied to a number of benchmark and real life problems with very good results.


2018 ◽  
Vol 6 (5) ◽  
pp. 459-472
Author(s):  
Xujiao Fan ◽  
Yong Xu ◽  
Xue Su ◽  
Jinhuan Wang

Abstract Using the semi-tensor product of matrices, this paper investigates cycles of graphs with application to cut-edges and the minimum spanning tree, and presents a number of new results and algorithms. Firstly, by defining a characteristic logical vector and using the matrix expression of logical functions, an algebraic description is obtained for cycles of graph, based on which a new necessary and sufficient condition is established to find all cycles for any graph. Secondly, using the necessary and sufficient condition of cycles, two algorithms are established to find all cut-edges and the minimum spanning tree, respectively. Finally, the study of an illustrative example shows that the results/algorithms presented in this paper are effective.


Sign in / Sign up

Export Citation Format

Share Document